Equilibrium Morphologies Research Articles

Thermodynamic stability of the meniscus oil film between air/solid/water and its relevance to flotation

The behavior of oil is an important aspect in the area of mineral flotation or oil-water separation. This paper proposes a specific phenomenon that a meniscus oil film may form between the air bubble and the solid surface under water surroundings. A thermodynamic system containing an air bubble, an oil droplet, a solid matrix, and water surroundings was constructed. The mechanical equilibrium state of the oil meniscus film was solved. The free energy difference ∆B between the oil film-formed state and a reference state based on the Gibbs surface thermodynamic theory is applied to characterize the stability of the meniscus oil film. The impacts of the oil-gas volume ratio and the interfacial tensions are taken into consideration. The results show that the equilibrium morphologies of the system are directly correlated with the interfacial tensions. A minimal ∆Bmin can be found at a certain volume ratio and the case ∆B<0 generally exists. It indicates the formation of oil film leads the system to a lower energy state which is thermodynamically stable. The batch flotation using glass beads and n-alkane collectors was conducted. The flotation results show that the oil can improve the particle recovery and the results can be well interpreted by the mechanism correlated to meniscus oil film.

Anisotropic Magnetic Polymeric Particles with a Controllable Structure via Seeded Emulsion Polymerization.

Magnetic polymer composites have been widely utilized in potential applications in material science, such as reduction of dyes, immunodiagnostics, biomedicals, and magnetically controllable photonic crystals owing to large surface areas, fast separation, and recyclable performance. In this work, anisotropic magnetic particles were prepared by seeded emulsion polymerization, with morphologies of "Fe3O4-shell", "hemisphere-like", "raspberry-like", "multiple lobes-like", and "sandwich-like". Poly(styrene/divinylbenzene/mono-2-(methacryloxy)ethyl succinate)@ Fe3O4 (P(St/DVB/MMES)@Fe3O4) were the seed microspheres, and P(St/DVB/MMES)@Fe3O4@polymer particles are achieved by seeded emulsion polymerizations. The morphology of the particles depends on polymerization conditions (monomer ratios and surfactant), particle properties, and so on. Then, the minimum surface free energy change principles were used to predict the equilibrium morphologies of the magnetic polymer composites. Through theory, the model gives the correct tendency and good agreement with the equilibrium morphology which was in tandem with TEM results. Lastly, after in situ surface deposition of Ag nanoparticles, magnetic composite particles with sandwich-like morphology were applied for the catalytic degradation of 4-nitrophenol (4-NP) reacting with NaBH4. The apparent rate coefficient is 0.0069 s-1, and it can keep mainly about 80% efficiency in catalysis after five cycles.

The surface and grain boundary properties of uranium boride: A DFT calculation

Uranium borides are currently being investigated as an accident tolerance fuel or advanced technology fuels (ATFs) to replace conventional UO2 fuel due to their high uranium density and high thermal conductivity. The surface properties of diverse facets of a crystal are pivotal for understanding different corrosion behaviors, fission gas bubble behaviors, and equilibrium morphologies. In this study, we employ density functional theory (DFT) calculations to investigate the surface properties of uranium borides. The surface orientations with maximum miller index up to 4, 1, and 2 for UB2, UB4 and UB12 were analyzed, respectively. Based on the calculated surface energies, the other surface properties of uranium borides were obtained through Wulff construction, including equilibrium morphology, dominant surface orientations, area-weighted surface energy and work function. Additionally, grain boundaries (GBs) have a significant impact on material properties, such as mechanical properties, corrosion behavior, and resistance to irradiation. Therefore, we use DFT calculations to determine the GB energies and work of separation for three low-Σ (7) symmetrical tilt GBs (STGB) and two twist GBs (TGB).

Modelling of the Solidifying Microstructure of Inconel 718: Quasi-Binary Approximation

The prediction of the equilibrium and metastable morphologies during the solidification of Ni-based superalloys on the mesoscopic scale can be performed using phase-field modeling. In the present paper, we apply the phase-field model to simulate the evolution of solidification microstructures depending on undercooling in a quasi-binary approximation. The results of modeling are compared with experimental data obtained on samples of the alloy Inconel 718 (IN718) processed using the electromagnetic leviatation (EML) technique. The final microstructure, concentration profiles of niobium, and the interface-velocity–undercooling relationship predicted by the phase field modeling are in good agreement with the experimental findings. The simulated microstructures and concentration fields can be used as inputs for the simulation of the precipitation of secondary phases.

Phase field modeling and computation of vesicle growth or shrinkage.

We present a phase field model for vesicle growth or shrinkage induced by an osmotic pressure due to a chemical potential gradient. The model consists of an Allen-Cahn equation describing the evolution of the phase field parameter that describes the shape of the vesicle and a Cahn-Hilliard-type equation describing the evolution of the ionic fluid. We establish conditions for vesicle growth or shrinkage via a common tangent construction using free energy curves. During the membrane deformation, the model ensures total mass conservation of the ionic fluid, and we weakly enforce a surface area constraint of the vesicle. We develop a stable numerical scheme and an efficient nonlinear multigrid solver to evolve the phase and concentration fields, and we use this to evolve the fields to near equilibrium for 2D vesicles. Convergence tests confirm an [Formula: see text] accuracy for our scheme and near-optimal convergence for our multigrid solver. Numerical results reveal that the diffuse interface model captures the main features of cell shape dynamics: for a growing vesicle, there exist circle-like equilibrium shapes if the concentration difference across the membrane and the initial osmotic pressure are large enough; while for a shrinking vesicle, there exists a rich collection of finger-like equilibrium morphologies.

Curvature and confinement effects on chiral liquid crystal morphologies.

Chiral liquid crystals (ChLCs) exhibit an inherent twist that originates at the molecular scale and can extend over multiple length scales when unconstrained. Under confinement, the twist is thwarted, leading to formation of defects in the molecular order that offer distinct optical responses and opportunities for colloidal driven assembly. Past studies have explored spheroidal confinement down to the nanoscopic regime, where curved boundaries produce surface defects to accommodate topological constraints and restrict the propagation of cuboidal defect networks. Similarly, strict confinement in channels and shells has been shown to give rise to escaped configurations and skyrmions. However, little is known about the role of extrinsic curvature in the development of cholesteric textures and Blue Phases (BP). In this paper, we examine the palette of morphologies that arises when ChLCs are confined in toroidal and cylindrical cavities. The equilibrium morphologies are obtained following an annealing strategy of a Landau-de Gennes free energy functional. Three dimensionless groups are identified to build phase diagrams: the natural twist, the ratio of elastic energies, and the circumscription of a BP cell. Curvature is shown to introduce helical features that are first observed as a Double Twist, and progress to Chiral Ribbons and, ultimately, Helical BP and BP. Chiral ribbons are examined as useful candidates for driven assembly given their tunability and robustness.

A general method for calculating solid/liquid interfacial free energies from atomistic simulations: Application to CaSO4·xH2O.

We present a general method for computing interfacial free energies from atomistic simulations, which is particularly suitable for solid/liquid interfaces. Our method uses an Einstein crystal as a universal reference state and is more flexible than previous approaches. Surfaces with dipoles, complex reconstructions, and miscible species are all easily accommodated within the framework. It may also be extended to calculating the relative free energies of different phases and other types of defect. We have applied our method to interfaces of bassanite and gypsum with water and obtained interfacial free energies of the order of 0.12J/m2, of which ∼45% is due to entropic contributions. Our calculations of the interfacial free energy of NaCl with water obtained a value of 0.13J/m2, of which only 19% is from entropic contributions. We have also predicted equilibrium morphologies for bassanite and gypsum that compare well with experiments and previous calculations.

Coupling Bulk Phase Separation of Disordered Proteins to Membrane Domain Formation in Molecular Simulations on a Bespoke Compute Fabric.

Phospholipid membranes surround the cell and its internal organelles, and their multicomponent nature allows the formation of domains that are important in cellular signalling, the immune system, and bacterial infection. Cytoplasmic compartments are also created by the phase separation of intrinsically disordered proteins into biomolecular condensates. The ubiquity of lipid membranes and protein condensates raises the question of how three-dimensional droplets might interact with two-dimensional domains, and whether this coupling has physiological or pathological importance. Here, we explore the equilibrium morphologies of a dilute phase of a model disordered protein interacting with an ideal-mixing, two-component lipid membrane using coarse-grained molecular simulations. We find that the proteins can wet the membrane with and without domain formation, and form phase separated droplets bound to membrane domains. Results from much larger simulations performed on a novel non-von-Neumann compute architecture called POETS, which greatly accelerates their execution compared to conventional hardware, confirm the observations. Reducing the wall clock time for such simulations requires new architectures and computational techniques. We demonstrate here an inter-disciplinary approach that uses real-world biophysical questions to drive the development of new computing hardware and simulation algorithms.

Nonlinear Transient and Steady State Stretching of Deflated Vesicles in Flow.

Membrane-bound vesicles and organelles exhibit a wide array of nonspherical shapes at equilibrium, including biconcave and tubular morphologies. Despite recent progress, the stretching dynamics of deflated vesicles is not fully understood, particularly far from equilibrium where complex nonspherical shapes undergo large deformations in flow. Here, we directly observe the transient and steady-state nonlinear stretching dynamics of deflated vesicles in extensional flow using a Stokes trap. Automated flow control is used to observe vesicle dynamics over a wide range of flow rates, shape anisotropy, and viscosity contrast. Our results show that deflated vesicle membranes stretch into highly deformed shapes in flow above a critical capillary number Cac1. We further identify a second critical capillary number Cac2, above which vesicle stretch diverges in flow. Vesicles are robust to multiple nonlinear stretch-relax cycles, evidenced by relaxation of dumbbell-shaped vesicles containing thin lipid tethers following flow cessation. An analytical model is developed for vesicle deformation in flow, which enables comparison of nonlinear steady-state stretching results with theories for different reduced volumes. Our results show that the model captures the steady-state stretching of moderately deflated vesicles; however, it underpredicts the steady-state nonlinear stretching of highly deflated vesicles. Overall, these results provide a new understanding of the nonlinear stretching dynamics and membrane mechanics of deflated vesicles in flow.

Interconversion-controlled liquid-liquid phase separation in a molecular chiral model.

Liquid-liquid phase separation of fluids exhibiting interconversion between alternative states has been proposed as an underlying mechanism for fluid polyamorphism and may be of relevance to the protein function and intracellular organization. However, molecular-level insight into the interplay between competing forces that can drive or restrict phase separation in interconverting fluids remains elusive. Here, we utilize an off-lattice model of enantiomers with tunable chiral interconversion and interaction properties to elucidate the physics underlying the stabilization and tunability of phase separation in fluids with interconverting states. We show that introducing an imbalance in the intermolecular forces between two enantiomers results in nonequilibrium, arrested phase separation into microdomains. We also find that in the equilibrium case, when all interaction forces are conservative, the growth of the phase domain is restricted only by the system size. In this case, we observe phase amplification, in which one of the two alternative phases grows at the expense of the other. These findings provide novel insights on how the interplay between dynamics and thermodynamics defines the equilibrium and steady-state morphologies of phase transitions in fluids with interconverting molecular or supramolecular states.

Controlling Equilibrium Morphologies of Bimetallic Nanostructures Using Thermal Dewetting via Phase-Field Modeling.

Herein, we report a computational model for the morphological evolution of bimetallic nanostructures in a thermal dewetting process, with a phase-field framework and superior optical, physical, and chemical properties compared to those of conventional nanostructures. The quantitative analysis of the simulation results revealed nano-cap, nano-ring, and nano-island equilibrium morphologies of the deposited material in thermal dewetting, and the morphologies depended on the gap between the spherical patterns on the substrate, size of the substrate, and deposition thickness. We studied the variations in the equilibrium morphologies of the nanostructures with the changes in the shape of the substrate pattern and the thickness of the deposited material. The method described herein can be used to control the properties of bimetallic nanostructures by altering their equilibrium morphologies using thermal dewetting.

Morphologies and dynamics of micro-droplet impact onto an idealised scratch

As inkjet technology develops to produce smaller droplets, substrate features such as accidental scratches or manufacturing defects can potentially affect the outcome of printing, particularly for printed electronics where continuous tracks are required. Here, the deposition of micro-droplets onto a scratch of commensurate size is studied. The scratch is considered as a groove of rectangular cross-section, with rectangular side ridges representing material displaced from the substrate, and seven equilibrium morphologies are identified as a result of inertial spreading, contact-line pinning, imbibition into the scratch and capillary flow. A regime map is constructed in terms of scratch depth and width, and theoretical estimates of the regime boundaries are developed by adapting droplet spreading laws for flat surfaces to account for liquid entering the scratches. Good agreement is seen with numerical results obtained using a graphical processing unit-accelerated three-dimensional multiphase lattice Boltzmann model validated against published experiments, and the influences of Reynolds number, Weber number and advancing and receding contact angles are explored. Negative and positive implications of the results for printing applications are discussed and illustrated via multiple-droplet simulations of printing across and along scratches.

Self-Assembly of Polymer Grafted Nanoparticles within Spherically Confined Diblock Copolymers.

Geometric confinement plays an important role in the generation of interesting microstructures on account of structural frustration and confinement-induced entropy loss. In the present study, self-consistent field calculations have been performed to examine the self-assembly behavior of a mixture of diblock copolymers and polymer grafted nanoparticles within a spherical confinement. The analysis is aimed at obtaining the equilibrium distribution of nanoparticles with a high degree of order. The ordered mesophases of diblock copolymers provide useful templates to achieve ordering of nanoparticles in a selective domain. Self-assembly of nanoparticles within frustrated diblock copolymers is found to be very different from the bulk. A rich variety of equilibrium morphologies are observed depending on the degree of confinement and the extent of particle loading. In addition, the role of particle size and selectivity along with the length and the number of polymer chains grafted onto the surface of nanoparticles are analyzed to understand the self-assembly behavior. The specific interest is to obtain the chiral structures out of achiral block copolymers subjected to spherical confinement. The realization of various captivating microstructures, such as chiral ordering of nanoparticles, is highly essential to produce advanced nanomaterials with superior physical properties.

How submarine channels (re)shape continental margins

ABSTRACTSubmarine landscapes, like their terrestrial counterparts, are sculpted by autogenic sedimentary processes toward morphologies at equilibrium with their allogenic controls. While submarine channels and nearby, inter-channel continental-margin areas share boundary conditions (e.g., terrestrial sediment supply, tectonic deformation), there are significant differences between the style, recurrence, and magnitude of their respective autogenic sedimentary processes. We predict that these process-based differences affect the rates of geomorphic change and equilibrium (i.e., graded) morphologies of submarine-channel and continental-margin longitudinal profiles. To gain insight into this proposed relationship, we document, classify (using machine learning), and analyze longitudinal profiles from 50 siliciclastic continental margins and associated submarine channels which represent a range of sediment-supply regimes and tectonic settings. These profiles tend to evolve toward smooth, lower-gradient longitudinal profiles, and we created a “smoothness” metric as a proxy for the relative maturity of these profiles toward the idealized equilibrium profile.Generally, higher smoothness values occur in systems with larger sediment supply, and the smoothness of channels typically exceeds that of the associated continental margin. We propose that the high rates of erosion, bypass, and deposition via sediment gravity flows act to smooth and mature channel profiles more rapidly than the surrounding continental margin, which is dominated by less-energetic diffusive sedimentary processes. Additionally, tectonic deformation will act to reduce the smoothness of these longitudinal profiles. Importantly, the relationship between total sediment supply and the difference between smoothness values of associated continental margins and submarine channels (the “smoothness Δ”) follows separate trends in passive and active tectonic settings, which we attribute to the variability in relative rates of smoothness development between channelized and inter-channel environments in the presence or absence of tectonic deformation. We propose two endmember pathways by which continental margins and submarine channels coevolve towards their respective equilibrium profiles with increased sediment supply: 1) Coupled Evolution Model (common in passive tectonic settings), in which the smoothness Δ increases only slightly before remaining static, and 2) Decoupled Evolution Model (common in active tectonic settings), in which the smoothness Δ increases more rapidly and to a greater final value. Our analysis indicates that the interaction of the allogenic factors of sediment supply and tectonic deformation with the autogenic sedimentary processes characteristic of channelized and inter-channel areas of the continental margin may account for much of the variability between coevolution pathways and depositional architectures.

Correction to “Nanosized Layered TOT Magnesium Silicates: Equilibrium Morphologies and Surface Speciation, a Computational and Experimental Study”

Correction to “Nanosized Layered TOT Magnesium Silicates: Equilibrium Morphologies and Surface Speciation, a Computational and Experimental Study”

Microstructural verification of the theoretically predicted morphologies of the NiAl–Cr pseudo-binary alloy systems and NiAl–Cr eutectic structure modification by Mo addition

Based on the NiAl–Cr pseudo-binary phase diagram, ranging from hypo- to hyper-eutectic areas, alloys with various compositions were produced by arc melting. The microstructures were compared with the theoretical predictions of Tang et al. (Chem Chem Phys 18(29):19773–19786, 2016) and they were proved to be in agreement. The partial substitution of Cr by Mo in three different compositions revealed eutectic and hypo-eutectic microstructures with the eutectic micro-constituent modified from fibrous to lamellar. The importance of T0-A2 and T0-B2 temperatures [the maximum temperatures under which, partitionless solidification of A2 and B2 phases respectively happens (Laughlin and Hono in Physical metallurgy, Elsevier, Amsterdam, 2014)] and their relation to Te (eutectic temperature) proved to be the dominant factor that shifts the microstructures to off equilibrium morphologies in the case of NiAl–Cr alloys.

Stability of the A15 phase in diblock copolymer melts

The self-assembly of block polymers into well-ordered nanostructures underpins their utility across fundamental and applied polymer science, yet only a handful of equilibrium morphologies are known with the simplest AB-type materials. Here, we report the discovery of the A15 sphere phase in single-component diblock copolymer melts comprising poly(dodecyl acrylate)-block-poly(lactide). A systematic exploration of phase space revealed that A15 forms across a substantial range of minority lactide block volume fractions (fL = 0.25 - 0.33) situated between the σ-sphere phase and hexagonally close-packed cylinders. Self-consistent field theory rationalizes the thermodynamic stability of A15 as a consequence of extreme conformational asymmetry. The experimentally observed A15-disorder phase transition is not captured using mean-field approximations but instead arises due to composition fluctuations as evidenced by fully fluctuating field-theoretic simulations. This combination of experiments and field-theoretic simulations provides rational design rules that can be used to generate unique, polymer-based mesophases through self-assembly.

Coarse-Grained Modelling and Temperature Effect on the Morphology of PS-b-PI Copolymer.

Spontaneous spatial organization behavior and the aggregate morphology of polystyrene-block-polyisoprene (PS-b-PI) copolymer were investigated. Molecular dynamic (MD) and mesoscopic simulations using the dynamic of mean field density functional theory (DDF) were adopted to investigate the morphology changes exhibited by this block copolymer (BCP). In the mesoscopic simulations, several atoms in repeating units were grouped together into a bead representing styrene or isoprene segments as a coarse-grained model. Inter-bead interactions and essential parameters for mesoscopic models were optimized from MD simulations. Study indicated that morphology alternations can be induced in this system at annealing temperature of 393, 493, and 533 K. From our simulations, lamellar, bicontinuous, and hexagonally packed cylindrical equilibrium morphologies were achieved. Our simulated morphologies agree well with the reported experimental evidence at the selected temperature. The process of aggregate formation and morphology evolution were concretely clarified.

A coarse grained simulation study on the morphology of ABA triblock copolymers

The Dissipative Particle Dynamics (DPD) simulation technique was used to elucidate the composition-dependent equilibrium morphological behavior of three different symmetric ABA triblock copolymers, which were; poly(ε-caprolactone)-poly(dimethylsiloxane)-poly(ε-caprolactone) (PCL-PDMS-PCL), poly(ε-caprolactone)-poly(ethylene oxide)-poly(ε-caprolactone) (PCL-PEO-PCL) and poly(L-lactide)-poly(dimethylsiloxane)-poly(L-lactide) (PLLA-PDMS-PLLA). These polymers were chosen due to their biomedical and biotechnological importance. Polymeric A and B blocks were modeled as connected chain of beads with varying incompatibility. The impact of the block incompatibilities on the microphase separation as well as on the equilibrium phase behaviors were investigated at the mesoscopic scale. A detailed visual analysis of the DPD images and constructed phase diagram showed that quite different equilibrium morphologies were attainable by controlling the molecular weights of the blocks and the strength of the intermolecular interaction between them. More compatible A and B blocks underwent lamellar to cylindrical and cylindrical to spherical phase transitions at lower B block concentrations. Our results clearly showed that, Flory–Huggins interaction parameter (χ) and degree of polymerization (N) were the only control parameters, which determined the shape and size of the phase domains, as well as the extent of equilibrium nanophase separation. Our DPD simulated morphologies were compared with experimental images obtained by Atomic Force Microscopy (AFM).

Self-Assembly Investigations of Sulfonated Poly(methyl methacrylate-block-styrene) Diblock Copolymer Thin Films

Poly(methyl methacrylate-block-styrene) block copolymers (BCs) of low dispersity were selectively sulfonated on the styrenic segment. Several combinations of degree of polymerization and volume fraction of each block were investigated to access different self-assembled morphologies. Thin films of the sulfonated block copolymers were prepared by spin-coating and exposed to solvent vapor (SVA) or thermal annealing (TA) to reach equilibrium morphologies. Atomic force microscopy (AFM) was employed for characterizing the films, which exhibited a variety of nanometric equilibrium and nonequilibrium morphologies. Highly sulfonated samples revealed the formation of a honeycomb-like morphology obtained in solution rather than by the self-assembly of the BC in the solid state. The described morphologies may be employed in applications such as templates for nanomanufacturing and as cover and binder of catalytic particles in fuel cells.